Solve sqrt{2}+sqrt{1/4}+1

$$\sqrt { 2 } + \sqrt { \frac { 1 } { 4 } } + 1$$

Evaluate

$$\sqrt{2}+\frac{3}{2}\approx 2.914213562$$

Solution Steps

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\sqrt{2}+\frac{1}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$\sqrt{2}+\frac{1}{2}+\frac{2}{2}$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\sqrt{2}+\frac{1+2}{2}$$

Add 1 and 2 to get 3.

$$\sqrt{2}+\frac{3}{2}$$